Automatic Dantzig–Wolfe reformulation of mixed integer programs

Mathematical Programming - Dantzig–Wolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs). However, the...     

A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size

We consider a two-dimensional cutting stock problem where stock of different sizes is available, and a set of rectangular items has to be obtained through two-staged guillotine cuts. We propose a heuristic algorithm, based on column generation, which requires as its subproblem the solution of a two-dimensional knapsack problem with two-staged guillotines cuts. A further contribution of the paper consists in the definition of a mixed integer linear programming model for the solution of this knapsack problem, as well as a heuristic procedure based on dynamic programming. Computational experiments show the effectiveness of the proposed approach, which obtains very small optimality gaps and outperforms the heuristic algorithm proposed by Cintra et al. [3].     

Synergistic electrocatalytic effect of nanostructured mixed films formed by functionalised gold nanoparticles and bisphthalocyanines

A synergistic electrocatalytic effect was observed in sensors where two electrocatalytic materials (functionalized gold nanoparticles and lutetium bisphthalocyanine) were co-deposited using the Langmuir–Blodgett technique. Films were prepared using a novel method where water soluble functionalised gold nanoparticles [(11-mercaptoundecyl)tetra(ethylene glycol)] (SAuNPs) were inserted in floating films of lutetium bisphthalocyanine (LuPc₂) and dimethyldioctadecylammonium bromide (DODAB) as the amphiphilic matrix. The formation of stable and homogeneous mixed films was confirmed by π-A isotherms, BAM, UV–vis and Raman spectroscopy, as well as by SEM and TEM microscopy. The synergistic effect towards hydroquinone of the electrodes modified with LuPc₂:DODAB/SAuNP was characterised by an increase in the intensity of the redox peaks and a reduction of the overpotential. This synergistic electrocatalytic effect arose from the interaction between the SAuNPs and the phthalocyanines that occur in the Langmuir–Blodgett films and from the high surface area provided by the nanostructured films. The sensitivity increased with the amount of LuPc₂ and SAuNPs inserted in the films and limits of detection in the range of 10⁻⁷ mol L⁻¹ were attained.     

Synergy between Printex nano-carbons and silver nanoparticles for sensitive estimation of antioxidant activity

We report on the synthesis, characterization and applications of a Printex L6 carbon-silver hybrid nanomaterial (PC-Ag), which was obtained using a polyol method. In addition, we also highlight the use of Printex L6 nano-carbon as a much cheaper alternative to the use of carbon nanotubes and graphene. The silver nanoparticles (AgNP) were prepared directly on the surface of the Printex 6L carbon “nanocarbon” material using ethylene glycol as the reducing agent. The hybrid nanomaterial was characterized by High-angle annular dark-field transmission electron microscopy (HAADF-TEM), energy–dispersive X-ray spectroscopy (EDX), selected area electron diffraction (SAED), Raman spectroscopy and cyclic voltammetry. Optimized electrocatalytic activity on glassy carbon electrode was reached for the architecture GC/PC-Ag, the silver nanoparticles with size ranging between 1 and 2 nm were well–distributed throughout the hybrid material. The synergy between PC nano-carbons and AgNPs was verified by detection of gallic acid (GA) at a low applied potential (0.091 V vs. Ag/AgCl). GA detection was performed in a concentration range between 5.0 × 10⁻⁷ and 8.5 × 10⁻⁶ mol L⁻¹, with a detection limit of 6.63 × 10⁻⁸ mol L⁻¹ (66.3 nmol L⁻¹), which is considerably lower than similar devices. The approach for fabricating the reproducible GC/PC-Ag electrodes is entirely generic and may be explored for other types of (bio)sensors and devices.     

Role of the intracellular cavity in potassium channel conductivity

The role of several fragments of the potassium channel KcsA has been examined by the Poisson-Nernst-Planck (PNP) theory. The efficiency of the computational method allowed comparing a large number of channel models, with different intracellular gate openings, partial atomic charges, and amino acid sequences. Perhaps counter-intuitively, the calculated ion current decreases when the mean radius of the entrance cavity increases. Widening of the vestibule, in fact, increases the volume accessible to water, which is the volume with a high dielectric constant. In turn, water screens the attractive charges of the P-loop backbone. The backbone charges of the M2 helixes instead oppose the entrance of potassium ions through a complicated mechanism that can be separated in the activity of two interfering dipoles. The conductance of the KcsA models increased when two neutral residues in M2 were mutated to glutamic acid, in agreement with experimental results (Brelidze, T. I.; Niu, X.; Magleby, K. L. PNAS 2003, 100, 9017-9022). As a general conclusion, a relation between channel conductance and potassium concentration in the intracellular cavity emerged. Although the ion transport is the result of the fine balance of a number of different effects, the experimental results can be reproduced quantitatively only on the basis of electrostatic forces, which are the only driving forces modeled by the PNP theory.     

A note on selective line-graphs and partition colorings

We extend a one-to-one correspondence between the set of all colorings of any graph and the set of all stable sets of an auxiliary graph, from graphs to partitioned graphs. This correspondence has an application to Selective Coloring and to Selective Max-Coloring.